## Problems

4.1 An OTEC is to deliver 100 MW to the bus bar. Its warm water comes from a solar-heated pond that is kept at 33 C. The water exhausted from the heat exchanger is returned to this same pond at a temperature of 31 C. (There is a slight heat loss in the pipes.) To reestablish the operating temperature, the pond must absorb heat from the sun. Assume an average (day and night) insolation of 250 W/m2 and an 80% absorption of solar energy by the water.

Cold water is pumped from the nearby abyss at a temperature of 8C. Refer to the figure for further information on the temperatures involved.

The warm water loses 1.84 K in going through the heat exchanger, while the cold water has its temperature raised by 1.35 K in its exchanger.

Assume that 80% of the remaining temperature difference appears across the turbine and that the rest is equally distributed as temperature differentials between the colder side of the warm heat exchanger (whose secondary side acts as an evaporator) and the turbine inlet and between the warmer side of the cold heat exchanger (whose secondary side acts as a condenser) and the turbine outlet (ATET and ATtc, in the figure).

Internal power for pumping and other ends is 40 MW. The efficiency of the turbine-generator combination is 90%. Estimate the rates of flow of warm and cold water.

What is the required surface of the heating pond, assuming no evaporation?

If the residence time of the water in the pond is three days, what depth must it have?

4.2 The Gulf Stream flows at a rate of 2-2 x 1012 m3/day. Its waters have a temperature of 25 C. Make a rough estimate of the area of the ocean that collects enough solar energy to permit this flow.

4.3 Assume that ammonia vaporizes in the evaporator of an OTEC at constant temperature (is this strictly true?). If the warm water enters the heat exchanger with a temperature AT1 higher than that of the boiling ammonia and leaves with a AT2, what is the mean AT? To check your results: If AT1 =4K and AT2 = 2K, then < AT> = 2-88K.

4.4 A 1.2-GWe nuclear power plant is installed near a river whose waters are used for cooling. The efficiency of the system is 20%. This is the ratio of electric output to heat input.

Technical reasons require that the coolant water exit the heat exchangers at a temperature of 80 C. It is proposed to use the warm coolant water to drive an OTEC-like plant. Assume: The river water is at 20 C,

The OTEC efficiency is one-half of the Carnot efficiency, and Half of the available AT is dropped across the turbine.

1. What is the flow rate of this water?

2. What is the maximum electric power that can be generated by such a plant?

4.5 An OTEC pumps 200 cubic meters of warm water per second through a heat exchanger in which the temperature drops by 1%. All the heat extracted is delivered to the ammonia boiler. The ammonia temperature at the turbine inlet is equal to the mean temperature of the water in the warm water heat exchanger minus 1 K. The condenser temperature is kept at 10 C by the cooling effect of 250 cubic meters per second of cold water. The efficiency of the turbine/generator system is 90%, and 12 MW of the produced electricity is used for pumping.

What must the intake temperature of the warm water be, so that a total of 20 MW of electricity is available for sale?

What must the intake temperature be so that the OTEC produces only exactly the amount of power needed for pumping?

4.6 Consider an OTEC whose turbine/generator has 100% mechanical efficiency. In other words, the system operates at the Carnot efficiency. Input temperature to the turbine is TH, and the output is at TC.

The input heat comes from a heat exchanger accepting water at THin and discharging it at a lower temperature, THout. The flow rate of warm water through this heat exchanger is VH.

The heat sink for the turbine is another heat exchanger taking in water at TCin and discharging it at a higher temperature, TCout. The flow rate of cold water through this heat exchanger is Vo. Refer to the following figure.

Heat

Heat

All the heat extracted from the warm water by the heat exchanger is transferred to the input of the turbine. All the heat rejected by the turbine is absorbed by the cold water heat exchanger and removed.

The following information is supplied:

Th is the mean of THin and THout.

To is the mean of TCin and TCout.

## Solar Panel Basics

Global warming is a huge problem which will significantly affect every country in the world. Many people all over the world are trying to do whatever they can to help combat the effects of global warming. One of the ways that people can fight global warming is to reduce their dependence on non-renewable energy sources like oil and petroleum based products.

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